. A toy company is selling novelty soccer balls of all sizes. If one soccer ball, with a radius of 5 cm, is placed in a box with all equal dimensions, as shown below, and the ball is touching the sides of the box, approximately how much empty space is inside the box?

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calculista calculista · Answer 1 · 2019-08-30T23:06:07+02:00

Answer:

The volume of the empty space is [tex]476.67\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the empty space inside the box is equal to the volume of the box minus the volume of the soccer ball

step 1

Find the volume of the box

The length side of the cube is equal to the diameter of the soccer ball

Let

b -----> the length side of the box

we have

[tex]b=2r=2(5)=10\ cm[/tex]

The volume of the box is equal to the volume of a cube

[tex]V=b^{3}[/tex]

substitute

[tex]V=10^{3}[/tex]

[tex]V=1,000\ cm^{3}[/tex]

step 2

Find the volume of the soccer ball

The volume of the sphere (soccer ball) is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=5\ cm[/tex]

[tex]\pi =3.14[/tex]

substitute

[tex]V=\frac{4}{3}(3.14)(5)^{3}[/tex]

[tex]V=523.33\ cm^{3}[/tex]

step 3

Find the volume of the empty space

[tex]V=1,000-523.33=476.67\ cm^{3}[/tex]